TSTP Solution File: ALG070+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : ALG070+1 : TPTP v8.1.2. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 30 16:01:11 EDT 2023
% Result : Theorem 0.20s 0.58s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 46 ( 11 unt; 8 typ; 0 def)
% Number of atoms : 118 ( 41 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 126 ( 46 ~; 40 |; 16 &)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 6 >; 2 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 56 ( 0 sgn; 34 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
sorti1: $i > $o ).
tff(decl_23,type,
op1: ( $i * $i ) > $i ).
tff(decl_24,type,
sorti2: $i > $o ).
tff(decl_25,type,
op2: ( $i * $i ) > $i ).
tff(decl_26,type,
h: $i > $i ).
tff(decl_27,type,
j: $i > $i ).
tff(decl_28,type,
esk1_0: $i ).
tff(decl_29,type,
esk2_0: $i ).
fof(co1,conjecture,
( ( ! [X1] :
( sorti1(X1)
=> sorti2(h(X1)) )
& ! [X2] :
( sorti2(X2)
=> sorti1(j(X2)) ) )
=> ~ ( ! [X3] :
( sorti1(X3)
=> ! [X4] :
( sorti1(X4)
=> h(op1(X3,X4)) = op2(h(X3),h(X4)) ) )
& ! [X5] :
( sorti2(X5)
=> ! [X6] :
( sorti2(X6)
=> j(op2(X5,X6)) = op1(j(X5),j(X6)) ) )
& ! [X7] :
( sorti2(X7)
=> h(j(X7)) = X7 )
& ! [X8] :
( sorti1(X8)
=> j(h(X8)) = X8 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax4,axiom,
~ ! [X1] :
( sorti2(X1)
=> ! [X2] :
( sorti2(X2)
=> ( op2(X1,X1) != X2
| op2(X1,X2) = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
fof(ax3,axiom,
! [X1] :
( sorti1(X1)
=> ! [X2] :
( sorti1(X2)
=> ( op1(X1,X1) != X2
| op1(X1,X2) = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
fof(ax1,axiom,
! [X1] :
( sorti1(X1)
=> ! [X2] :
( sorti1(X2)
=> sorti1(op1(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
fof(c_0_4,negated_conjecture,
~ ( ( ! [X1] :
( sorti1(X1)
=> sorti2(h(X1)) )
& ! [X2] :
( sorti2(X2)
=> sorti1(j(X2)) ) )
=> ~ ( ! [X3] :
( sorti1(X3)
=> ! [X4] :
( sorti1(X4)
=> h(op1(X3,X4)) = op2(h(X3),h(X4)) ) )
& ! [X5] :
( sorti2(X5)
=> ! [X6] :
( sorti2(X6)
=> j(op2(X5,X6)) = op1(j(X5),j(X6)) ) )
& ! [X7] :
( sorti2(X7)
=> h(j(X7)) = X7 )
& ! [X8] :
( sorti1(X8)
=> j(h(X8)) = X8 ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_5,negated_conjecture,
! [X17,X18,X19,X20,X21,X22,X23,X24] :
( ( ~ sorti1(X17)
| sorti2(h(X17)) )
& ( ~ sorti2(X18)
| sorti1(j(X18)) )
& ( ~ sorti1(X19)
| ~ sorti1(X20)
| h(op1(X19,X20)) = op2(h(X19),h(X20)) )
& ( ~ sorti2(X21)
| ~ sorti2(X22)
| j(op2(X21,X22)) = op1(j(X21),j(X22)) )
& ( ~ sorti2(X23)
| h(j(X23)) = X23 )
& ( ~ sorti1(X24)
| j(h(X24)) = X24 ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
cnf(c_0_6,negated_conjecture,
( j(h(X1)) = X1
| ~ sorti1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_7,negated_conjecture,
( sorti1(j(X1))
| ~ sorti2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,negated_conjecture,
( j(h(j(X1))) = j(X1)
| ~ sorti2(X1) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_9,negated_conjecture,
( sorti2(h(X1))
| ~ sorti1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,negated_conjecture,
( j(h(j(h(X1)))) = j(h(X1))
| ~ sorti1(X1) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_11,negated_conjecture,
( j(h(j(h(j(X1))))) = j(h(j(X1)))
| ~ sorti2(X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_7]) ).
cnf(c_0_12,negated_conjecture,
( j(h(j(h(j(h(X1)))))) = j(h(j(h(X1))))
| ~ sorti1(X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_9]) ).
fof(c_0_13,plain,
( sorti2(esk1_0)
& sorti2(esk2_0)
& op2(esk1_0,esk1_0) = esk2_0
& op2(esk1_0,esk2_0) != esk1_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax4])])]) ).
fof(c_0_14,plain,
! [X13,X14] :
( ~ sorti1(X13)
| ~ sorti1(X14)
| op1(X13,X13) != X14
| op1(X13,X14) = X13 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax3])])]) ).
cnf(c_0_15,negated_conjecture,
( j(h(j(h(j(h(j(X1))))))) = j(h(j(h(j(X1)))))
| ~ sorti2(X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_7]) ).
cnf(c_0_16,negated_conjecture,
( h(j(X1)) = X1
| ~ sorti2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_17,plain,
sorti2(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
( op1(X1,X2) = X1
| ~ sorti1(X1)
| ~ sorti1(X2)
| op1(X1,X1) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_19,plain,
! [X9,X10] :
( ~ sorti1(X9)
| ~ sorti1(X10)
| sorti1(op1(X9,X10)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax1])])]) ).
cnf(c_0_20,negated_conjecture,
( j(op2(X1,X2)) = op1(j(X1),j(X2))
| ~ sorti2(X1)
| ~ sorti2(X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_21,plain,
sorti2(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_22,negated_conjecture,
( sorti1(j(h(j(h(j(X1))))))
| ~ sorti2(h(j(h(j(h(j(X1)))))))
| ~ sorti2(X1) ),
inference(spm,[status(thm)],[c_0_7,c_0_15]) ).
cnf(c_0_23,negated_conjecture,
h(j(esk2_0)) = esk2_0,
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_24,plain,
( op1(X1,op1(X1,X1)) = X1
| ~ sorti1(op1(X1,X1))
| ~ sorti1(X1) ),
inference(er,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
( sorti1(op1(X1,X2))
| ~ sorti1(X1)
| ~ sorti1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,negated_conjecture,
( op1(j(X1),j(esk1_0)) = j(op2(X1,esk1_0))
| ~ sorti2(X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,plain,
op2(esk1_0,esk1_0) = esk2_0,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_28,negated_conjecture,
h(j(esk1_0)) = esk1_0,
inference(spm,[status(thm)],[c_0_16,c_0_21]) ).
cnf(c_0_29,negated_conjecture,
( h(op1(X1,X2)) = op2(h(X1),h(X2))
| ~ sorti1(X1)
| ~ sorti1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_30,negated_conjecture,
sorti1(j(esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_23]),c_0_23]),c_0_23]),c_0_17]),c_0_17])]) ).
cnf(c_0_31,plain,
( op1(X1,op1(X1,X1)) = X1
| ~ sorti1(X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_32,negated_conjecture,
op1(j(esk1_0),j(esk1_0)) = j(esk2_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_21]),c_0_27]) ).
cnf(c_0_33,negated_conjecture,
sorti1(j(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_28]),c_0_28]),c_0_28]),c_0_28]),c_0_21]),c_0_21])]) ).
cnf(c_0_34,negated_conjecture,
( h(op1(X1,j(esk2_0))) = op2(h(X1),esk2_0)
| ~ sorti1(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_23]) ).
cnf(c_0_35,negated_conjecture,
op1(j(esk1_0),j(esk2_0)) = j(esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]) ).
cnf(c_0_36,plain,
op2(esk1_0,esk2_0) != esk1_0,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_37,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_33]),c_0_35]),c_0_28]),c_0_28]),c_0_36]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG070+1 : TPTP v8.1.2. Released v2.7.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 03:08:29 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 0.20/0.58 % Version : CSE_E---1.5
% 0.20/0.58 % Problem : theBenchmark.p
% 0.20/0.58 % Proof found
% 0.20/0.58 % SZS status Theorem for theBenchmark.p
% 0.20/0.58 % SZS output start Proof
% See solution above
% 0.20/0.59 % Total time : 0.008000 s
% 0.20/0.59 % SZS output end Proof
% 0.20/0.59 % Total time : 0.011000 s
%------------------------------------------------------------------------------